Subgroups — C₁₃₉×#37317 #48031913

Order 35584.

2018 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2751×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2714×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2714×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2688×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2615×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2324×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
26	#400×C₁₃₉	C₂²	1	4	yes	—
27	#397×C₁₃₉	C₂²	1	4	yes	—
28	#397×C₁₃₉	C₂²	1	4	yes	—
29	#397×C₁₃₉	C₂²	1	4	yes	—
30	#394×C₁₃₉	C₂²	1	4	yes	—
31	#394×C₁₃₉	C₂²	1	4	yes	—
32	#394×C₁₃₉	C₂²	1	4	yes	—
33	#393×C₁₃₉	C₂²	1	4	yes	—
34	#392×C₁₃₉	C₂²	1	4	yes	—
35	#392×C₁₃₉	C₂²	1	4	yes	—
36	#392×C₁₃₉	C₂²	1	4	yes	—
37	#392×C₁₃₉	C₂²	1	4	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#390×C₁₃₉	C₂²	1	4	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	4	yes	—
44	#390×C₁₃₉	C₂²	1	4	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#388×C₁₃₉	C₂²	1	4	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#387×C₁₃₉	C₂²	1	4	yes	—
50	#387×C₁₃₉	C₂²	1	4	yes	—
51	#386×C₁₃₉	C₂²	1	2	yes	—
52	#386×C₁₃₉	C₂²	1	2	yes	—
53	#386×C₁₃₉	C₂²	1	4	yes	—
54	#386×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#385×C₁₃₉	C₂²	1	4	yes	—
57	#385×C₁₃₉	C₂²	1	4	yes	—
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic
59	#382×C₁₃₉	C₂²	1	1	yes	characteristic
60	#381×C₁₃₉	C₂²	1	4	yes	—
61	#380×C₁₃₉	C₂²	1	2	yes	—
62	#380×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
67	C₂×#41×C₁₃₉	—	2	4	no	—
68	C₂×#41×C₁₃₉	—	4	2	no	—
69	C₂×#41×C₁₃₉	—	4	2	no	—
70	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
82	#127×C₁₃₉	—	4	2	no	—
83	#126×C₁₃₉	—	4	8	no	—
84	#125×C₁₃₉	—	4	2	no	—
85	#121×C₁₃₉	—	2	8	no	—
86	#121×C₁₃₉	—	4	8	no	—
87	#121×C₁₃₉	—	4	4	no	—
88	#121×C₁₃₉	—	4	4	no	—
89	#121×C₁₃₉	—	4	8	no	—
90	C₄×D₄×C₁₃₉	—	4	4	no	—
91	#117×C₁₃₉	—	4	2	no	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₉	—	4	2	no	—
118	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	2	yes	—
125	#95×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	2	yes	—
132	#95×C₁₃₉	C₂³	1	2	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	#41×C₁₃₉	—	4	16	no	—
138	C₂×Q₈×C₁₃₉	—	2	2	no	—
139	C₂×Q₈×C₁₃₉	—	4	1	no	—
140	C₂×Q₈×C₁₃₉	—	4	1	no	—
141	C₂×D₄×C₁₃₉	—	2	4	no	—
142	C₂×D₄×C₁₃₉	—	2	8	no	—
143	C₂×D₄×C₁₃₉	—	2	4	no	—
144	C₂×D₄×C₁₃₉	—	2	2	no	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	8	no	—
148	C₂×D₄×C₁₃₉	—	4	1	no	—
149	C₂×D₄×C₁₃₉	—	4	1	no	—
150	C₂×D₄×C₁₃₉	—	4	2	no	—
151	C₂×D₄×C₁₃₉	—	4	2	no	—
152	C₂×D₄×C₁₃₉	—	4	4	no	—
153	C₂×D₄×C₁₃₉	—	4	4	no	—
154	C₂×D₄×C₁₃₉	—	4	4	no	—
155	C₂×D₄×C₁₃₉	—	4	4	no	—
156	C₂×D₄×C₁₃₉	—	4	4	no	—
157	C₂×D₄×C₁₃₉	—	4	4	no	—
158	C₂×D₄×C₁₃₉	—	4	4	no	—
159	C₂×D₄×C₁₃₉	—	4	4	no	—
160	C₂×D₄×C₁₃₉	—	4	4	no	—
161	C₂×D₄×C₁₃₉	—	4	4	no	—
162	C₂²×C₄×C₁₃₉	—	2	2	no	—
163	C₂²×C₄×C₁₃₉	—	2	2	no	—
164	C₂²×C₄×C₁₃₉	—	2	4	no	—
165	C₂²×C₄×C₁₃₉	—	2	4	no	—
166	C₂²×C₄×C₁₃₉	—	2	4	no	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	4	2	no	—
169	C₂²×C₄×C₁₃₉	—	4	2	no	—
170	C₂²×C₄×C₁₃₉	—	4	4	no	—
171	C₂²×C₄×C₁₃₉	—	4	4	no	—
172	C₂²×C₄×C₁₃₉	—	4	4	no	—
173	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₁₃₉	—	2	4	no	—
185	C₄⋊C₄×C₁₃₉	—	2	4	no	—
186	C₄⋊C₄×C₁₃₉	—	2	4	no	—
187	C₄⋊C₄×C₁₃₉	—	2	8	no	—
188	C₄⋊C₄×C₁₃₉	—	2	8	no	—
189	C₄⋊C₄×C₁₃₉	—	4	2	no	—
190	C₄⋊C₄×C₁₃₉	—	4	4	no	—
191	C₄⋊C₄×C₁₃₉	—	4	4	no	—
192	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
196	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
197	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
199	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
202	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
203	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
204	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
205	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
207	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
208	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
209	C₄²×C₁₃₉	—	2	2	no	—
210	C₄²×C₁₃₉	—	2	2	no	—
211	C₄²×C₁₃₉	—	2	4	no	—
212	C₄²×C₁₃₉	—	4	2	no	—
213	C₄²×C₁₃₉	—	4	4	no	—
214	C₂³×C₁₃₉	—	2	1	no	—
215	C₂³×C₁₃₉	—	2	1	no	—
216	C₂³×C₁₃₉	—	2	2	no	—
217	C₂³×C₁₃₉	—	2	2	no	—
218	C₂³×C₁₃₉	—	2	4	no	—
219	C₂³×C₁₃₉	—	2	2	no	—
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	4	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	4	no	—
225	C₂³×C₁₃₉	—	2	4	no	—
226	C₂³×C₁₃₉	—	2	2	no	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	4	no	—
229	C₂³×C₁₃₉	—	2	2	no	—
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	4	no	—
232	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
233	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃₉	—	4	4	no	—
235	D₄×C₁₃₉	—	4	4	no	—
236	D₄×C₁₃₉	—	4	8	no	—
237	D₄×C₁₃₉	—	4	8	no	—
238	D₄×C₁₃₉	—	8	8	no	—
239	D₄×C₁₃₉	—	8	8	no	—
240	D₄×C₁₃₉	—	8	8	no	—
241	D₄×C₁₃₉	—	8	8	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	1	no	—
244	C₂×C₄×C₁₃₉	—	2	1	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	8	no	—
247	C₂×C₄×C₁₃₉	—	2	4	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	4	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	4	no	—
262	C₂×C₄×C₁₃₉	—	2	4	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	4	no	—
268	C₂×C₄×C₁₃₉	—	4	8	no	—
269	C₂×C₄×C₁₃₉	—	4	8	no	—
270	C₂×C₄×C₁₃₉	—	8	8	no	—
271	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
272	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
274	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₁₃₉	—	2	2	no	—
277	C₂²×C₁₃₉	—	2	2	no	—
278	C₂²×C₁₃₉	—	2	2	no	—
279	C₂²×C₁₃₉	—	4	2	no	—
280	C₂²×C₁₃₉	—	4	2	no	—
281	C₂²×C₁₃₉	—	4	2	no	—
282	C₂²×C₁₃₉	—	4	4	no	—
283	C₂²×C₁₃₉	—	4	4	no	—
284	C₂²×C₁₃₉	—	4	2	no	—
285	C₂²×C₁₃₉	—	4	4	no	—
286	C₂²×C₁₃₉	—	4	2	no	—
287	C₂²×C₁₃₉	—	4	4	no	—
288	C₂²×C₁₃₉	—	4	2	no	—
289	C₂²×C₁₃₉	—	4	4	no	—
290	C₂²×C₁₃₉	—	4	2	no	—
291	C₂²×C₁₃₉	—	4	4	no	—
292	C₂²×C₁₃₉	—	4	2	no	—
293	C₂²×C₁₃₉	—	4	4	no	—
294	C₂²×C₁₃₉	—	4	2	no	—
295	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
296	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
297	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₂²×C₁₃₉	#585	1	2	yes	—
300	C₄×C₁₃₉	—	2	2	no	—
301	C₄×C₁₃₉	—	2	4	no	—
302	C₄×C₁₃₉	—	4	2	no	—
303	C₄×C₁₃₉	—	4	4	no	—
304	C₄×C₁₃₉	—	4	2	no	—
305	C₄×C₁₃₉	—	4	4	no	—
306	C₄×C₁₃₉	—	4	2	no	—
307	C₄×C₁₃₉	—	4	2	no	—
308	C₄×C₁₃₉	—	4	4	no	—
309	C₄×C₁₃₉	#538	1	4	yes	—
310	C₂×C₁₃₉	—	4	2	no	—
311	C₂×C₁₃₉	—	8	2	no	—
312	C₂×C₁₃₉	—	8	4	no	—
313	C₂×C₁₃₉	C₂×#538	1	1	yes	characteristic
314	C₂×C₁₃₉	#3508	1	1	yes	characteristic
315	C₂×C₁₃₉	#3512	1	1	yes	characteristic
316	C₂×C₁₃₉	#3542	1	2	yes	—
317	C₂×C₁₃₉	#3546	1	2	yes	—
318	#37317	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₁₃₉	#37317	1	1	yes	characteristic, direct product factor, Sylow
320	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
321	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
322	#2751	C₂×C₁₃₉	1	4	yes	complemented
323	#2714	C₂×C₁₃₉	1	4	yes	complemented
324	#2714	C₂×C₁₃₉	1	4	yes	complemented
325	#2688	C₂×C₁₃₉	1	4	yes	complemented
326	#2615	C₂×C₁₃₉	1	2	yes	complemented
327	#2496	C₂×C₁₃₉	1	2	yes	complemented
328	#2490	C₂×C₁₃₉	1	2	yes	complemented
329	#2428	C₂×C₁₃₉	1	2	yes	complemented
330	#2420	C₂×C₁₃₉	1	2	yes	complemented
331	#2324	C₂×C₁₃₉	1	2	yes	complemented
332	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
333	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
334	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
335	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
336	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
337	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
338	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
339	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
340	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
341	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
342	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
343	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
345	#400	C₂²×C₁₃₉	1	4	yes	—
346	#397	C₂²×C₁₃₉	1	4	yes	—
347	#397	C₂²×C₁₃₉	1	4	yes	—
348	#397	C₂²×C₁₃₉	1	4	yes	—
349	#394	C₂²×C₁₃₉	1	4	yes	—
350	#394	C₂²×C₁₃₉	1	4	yes	—
351	#394	C₂²×C₁₃₉	1	4	yes	—
352	#393	C₂²×C₁₃₉	1	4	yes	—
353	#392	C₂²×C₁₃₉	1	4	yes	—
354	#392	C₂²×C₁₃₉	1	4	yes	—
355	#392	C₂²×C₁₃₉	1	4	yes	—
356	#392	C₂²×C₁₃₉	1	4	yes	—
357	#391	C₂²×C₁₃₉	1	2	yes	—
358	#390	C₂²×C₁₃₉	1	2	yes	—
359	#390	C₂²×C₁₃₉	1	4	yes	—
360	#390	C₂²×C₁₃₉	1	2	yes	—
361	#390	C₂²×C₁₃₉	1	4	yes	—
362	#390	C₂²×C₁₃₉	1	4	yes	—
363	#390	C₂²×C₁₃₉	1	2	yes	—
364	#389	C₂²×C₁₃₉	1	2	yes	—
365	#389	C₂²×C₁₃₉	1	2	yes	—
366	#388	C₂²×C₁₃₉	1	4	yes	—
367	#388	C₂²×C₁₃₉	1	4	yes	—
368	#387	C₂²×C₁₃₉	1	4	yes	—
369	#387	C₂²×C₁₃₉	1	4	yes	—
370	#386	C₂²×C₁₃₉	1	4	yes	—
371	#386	C₂²×C₁₃₉	1	4	yes	—
372	#386	C₂²×C₁₃₉	1	4	yes	—
373	#386	C₂²×C₁₃₉	1	2	yes	—
374	#386	C₂²×C₁₃₉	1	2	yes	—
375	#385	C₂²×C₁₃₉	1	4	yes	—
376	#385	C₂²×C₁₃₉	1	4	yes	—
377	#384	C₂²×C₁₃₉	1	1	yes	characteristic
378	#382	C₂²×C₁₃₉	1	1	yes	characteristic
379	#381	C₂²×C₁₃₉	1	4	yes	—
380	#380	C₂²×C₁₃₉	1	2	yes	—
381	#380	C₂²×C₁₃₉	1	2	yes	—
382	#380	C₂²×C₁₃₉	1	2	yes	—
383	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
384	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
385	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
386	C₂×#41	—	2	4	no	—
387	C₂×#41	—	4	2	no	—
388	C₂×#41	—	4	2	no	—
389	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
391	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
392	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
401	#127	—	4	2	no	—
402	#126	—	4	8	no	—
403	#125	—	4	2	no	—
404	#121	—	2	8	no	—
405	#121	—	4	8	no	—
406	#121	—	4	4	no	—
407	#121	—	4	4	no	—
408	#121	—	4	8	no	—
409	C₄×D₄	—	4	4	no	—
410	#117	—	4	2	no	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
436	C₂×C₄²	—	4	2	no	—
437	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
438	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
441	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
442	#95	C₂³×C₁₃₉	1	2	yes	—
443	#95	C₂³×C₁₃₉	1	2	yes	—
444	#95	C₂³×C₁₃₉	1	2	yes	—
445	#95	C₂³×C₁₃₉	1	2	yes	—
446	#95	C₂³×C₁₃₉	1	4	yes	—
447	#95	C₂³×C₁₃₉	1	4	yes	—
448	#95	C₂³×C₁₃₉	1	4	yes	—
449	#95	C₂³×C₁₃₉	1	4	yes	—
450	#95	C₂³×C₁₃₉	1	4	yes	—
451	#95	C₂³×C₁₃₉	1	4	yes	—
452	#95	C₂³×C₁₃₉	1	4	yes	—
453	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
454	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
455	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
456	#41	—	4	16	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	4	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	—	4	1	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	4	4	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂×D₄	—	4	4	no	—
476	C₂×D₄	—	4	4	no	—
477	C₂×D₄	—	4	4	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	—	4	4	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	4	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	—	4	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₂²⋊C₄	—	4	4	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	4	4	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
552	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
553	Q₈	—	4	4	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	8	no	—
556	D₄	—	4	8	no	—
557	D₄	—	8	8	no	—
558	D₄	—	8	8	no	—
559	D₄	—	8	8	no	—
560	D₄	—	8	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	—	8	8	no	—
590	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
591	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
592	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
593	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
594	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	2	no	—
614	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
615	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
616	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
617	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
618	C₂²	#585×C₁₃₉	1	2	yes	—
619	C₄	—	2	4	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	4	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	4	no	—
628	C₄	#538×C₁₃₉	1	4	yes	—
629	C₂	—	4	2	no	—
630	C₂	—	8	4	no	—
631	C₂	—	8	2	no	—
632	C₂	C₂×#538×C₁₃₉	1	1	yes	characteristic
633	C₂	#3508×C₁₃₉	1	1	yes	characteristic
634	C₂	#3512×C₁₃₉	1	1	yes	characteristic
635	C₂	#3542×C₁₃₉	1	2	yes	—
636	C₂	#3546×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #2856×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2751×C₁₃₉	C₂	semidirect
4. #2714×C₁₃₉	C₂	semidirect
5. #2714×C₁₃₉	C₂	semidirect
6. #2688×C₁₃₉	C₂	semidirect
7. #2615×C₁₃₉	C₂	semidirect
8. #2496×C₁₃₉	C₂	semidirect
9. #2490×C₁₃₉	C₂	semidirect
10. #2428×C₁₃₉	C₂	semidirect
11. #2420×C₁₃₉	C₂	semidirect
12. #2324×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
318. #37317	C₁₃₉	direct (N × H)
319. C₁₃₉	#37317	direct (N × H)
320. #2856	C₂×C₁₃₉	semidirect
321. #2851	C₂×C₁₃₉	semidirect
322. #2751	C₂×C₁₃₉	semidirect
323. #2714	C₂×C₁₃₉	semidirect
324. #2714	C₂×C₁₃₉	semidirect
325. #2688	C₂×C₁₃₉	semidirect
326. #2615	C₂×C₁₃₉	semidirect
327. #2496	C₂×C₁₃₉	semidirect
328. #2490	C₂×C₁₃₉	semidirect
329. #2428	C₂×C₁₃₉	semidirect
330. #2420	C₂×C₁₃₉	semidirect
331. #2324	C₂×C₁₃₉	semidirect
332. #2297	C₂×C₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#2856×C₁₃₉	2
#2851×C₁₃₉	2
#2751×C₁₃₉	2
#2714×C₁₃₉	2
#2688×C₁₃₉	2
#2615×C₁₃₉	2
#2496×C₁₃₉	2
#2490×C₁₃₉	2
#2428×C₁₃₉	2
#2420×C₁₃₉	2
#2324×C₁₃₉	2
#2297×C₁₃₉	2
#37317	139

Subgroups — C139×#37317 #48031913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37317 #48031913